Thermodynamic analysis of energy density in pressure retarded osmosis: The impact of solution volumes and costs

A general method was developed for estimating the volumetric energy efficiency of pressure retarded osmosis via pressure-volume analysis of a membrane process. The resulting model requires only the osmotic pressure, π, and mass fraction, w, of water in the concentrated and dilute feed solutions to estimate the maximum achievable specific energy density, u, as a function of operating pressure. The model is independent of any membrane or module properties. This method utilizes equilibrium analysis to specify the volumetric mixing fraction of concentrated and dilute solution as a function of operating pressure, and provides results for the total volumetric energy density of similar order to more complex models for the mixing of seawater and riverwater. Within the framework of this analysis, the total volumetric energy density is maximized, for an idealized case, when the operating pressure is π/(1+w-1), which is lower than the maximum power density operating pressure, δπ/2, derived elsewhere, and is a function of the solute osmotic pressure at a given mass fraction. It was also found that a minimum 1.45. kmol of ideal solute is required to produce 1. kWh of energy while a system operating at "maximum power density operating pressure" requires at least 2.9. kmol. Utilizing this methodology, it is possible to examine the effects of volumetric solution cost, operation of a module at various pressure, and operation of a constant pressure module with various feed.